f is a differentiable function such that...

f is a differentiable function such that `x= f (t ^(2)), y= f (t ^(3)) and f (1) ne 0 if ((d ^(2) y)/(dx ^(2))_(t=1))=`

`3/4 ((f''(1)+f (1))/((f' (1))^(2)))`

`3/4 ((f (1). f '(1) -f'(1))/(f (f'(1))^(2)))`

`4/3 (f'(1))/((f'(1))^(2))`

`4/3((f '(1)f''(1) -f' (1))/((f'(1))^(2)))`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|36 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|30 Videos
COMPOUND ANGLES
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
DETERMINANTS
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

f is a differentiable function such that x=f(t^2),y=f(t^3) and f'(1)!=0 if ((d^2y)/(dx^2))_(t=1) =

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):

Let x=f(t) and y=g(t), where x and y are twice differentiable function. If f'(0)= g'(0) =f''(0) = 2. g''(0) = 6, then the value of ((d^(2)y)/(dx^(2)))_(t=0) is equal to

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) is

If f(x) is differentiable function in the interval (0,oo) such that f(1) = 1 and lim_(trarrx) (t^(2)f(x)-x^(2)(t))/(t-x)=1 for each x gt 0 , then f((3)/(2)) is equal tv

If f:RrarrR,f(x) is a differentiable function such that (f(x))^(2)=e^(2)+int_(0)^(x)(f(t)^(2)+(f'(t))^(2))dtAAx inR . The values f(1) can take is/are

Let f(x) be a differentiable function such that int_(t)^(t^(2))xf(x)dx=(4)/(3)t^(3)-(4t)/(3)AA t ge0 , then f(1) is equal to

Let f :R ^(+) to R be a differentiable function with f (1)=3 and satisfying : int _(1) ^(xy) f(t) dt =y int_(1) ^(x) f (t) dt +x int_(1) ^(y) f (t) dt AA x, y in R^(+), then f (e) =

VIKAS GUPTA (BLACK BOOK) ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)

f is a differentiable function such that x= f (t ^(2)), y= f (t ^(3)) ...
Text Solution
|
Let f (x)= {{:(ax (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...
Text Solution
|
If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...
Text Solution
|
If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(3)), where k ...
Text Solution
|
The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix)...
Text Solution
|
If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...
Text Solution
|
In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...
Text Solution
|
Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim( n to oo) (f...
Text Solution
|
Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...
Text Solution
|
If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable...
Text Solution
|
Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...
Text Solution
|
If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...
Text Solution
|
f (x) =a cos (pix)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...
Text Solution
|
Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...
Text Solution
|
Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...
Text Solution
|
If y=e^(2 sin ^(-1)x) then |((x ^(2) -1) y ^('') +xy')/(y)| is equal t...
Text Solution
|
Let f be continuous function on [0,oo) such that lim (x to oo) (f(x)+ ...
Text Solution
|
Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...
Text Solution
|
In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...
Text Solution
|
Let f :R to R be a differentiable function satisfying: f (xy) =(f(x)...
Text Solution
|
For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...
Text Solution
|